Question

An orthogonal matrix is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

A square matrix is to be orthogonal matrix if A'A = I = AA'

$\Rightarrow \begin{array}{c}A=\left[\begin{array}{cc}cos\alpha & sin\alpha \\ -sin\alpha & cos\alpha \end{array}\right],A^{\prime }=\left[\begin{array}{cc}cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{array}\right]\end{array}$

$\Rightarrow \begin{array}{c}A{A}^{\prime }=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],A^{\prime }A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\end{array}$

$\therefore A{A}^{\prime }=A^{\prime }A=I$